Periodic solutions of higher-dimensional discrete systems. (English) Zbl 1073.39010

Zhou, Zhan; Yu, Jianshe; Guo, Zhiming

Proc. R. Soc. Edinb., Sect. A, Math. 134, No. 5, 1013-1022 (2004).

The authors consider the second-order discrete system \[ \Delta^2X_{n-1}+ f(n, X_n)= 0,\quad n\in\mathbb{Z},\tag{1} \] where \(f\in C(\mathbb{R}\times \mathbb{R}^m, \mathbb{R}^m)\), \(f(t+ M,\mathbb{Z})= f(t,\mathbb{Z})\) for any \((t,\mathbb{Z})\in \mathbb{R}\times \mathbb{R}^m\) and \(M\) is a positive integer. The existence of \(M\) periodic solutions of (1) is proved.

Reviewer: Stefan Balint (Timişoara)

MSC:

39A11	Stability of difference equations (MSC2000)
39A12	Discrete version of topics in analysis
34C25	Periodic solutions to ordinary differential equations

Keywords:

second-order discrete system; periodic solution